PROBLEMS OF GEOCOSMOS

Proceedings of the 7th International Conference "Problems of Geocosmos" (St. Petersburg, Russia, 26-30 May 2008)
We compute topological invariants both for original and inverted magnetograms and for original and inverted
image of Holder maps. As a result we get four couple of such numbers. So, for active region which was
observed during five days we obtain time series of Betti numbers with near 80 values.
Results
For exploration of the original magnetogram it was decided to investigate difference of corresponding Betti
numbers for positive and negative images. We found out the distinction in variation of such difference for Xflare
active region and flare-quiet active region. For flare quiet regions the differences oscillates near zero, but
for flare active regions Betti differences were strongly above or under the zero level (Figure 6). From
physical point of view such behavior signals that during the activity in region there is a prevalence of one
polarity before another.
p n
-β0
β 0
p n
-βi ; i=0,1
β i
700
600
500
400
300
200
100
1500
1000
500
0
-500
0 10 20 30 40 50 60 70 80
# fits
flare-quiet active region
-1000
0 10 20 30 40
Figure 5
For given image digital piece β 0 =1, β 1=1.
Cycle I and J are
homologous. Cycle K retracts to point
# fits
X-flare active region
p n
-β1
β 1
500
0
-500
-1000
-1500
-2000
-2500
0 10 20 30 40 50 60 70 80 90
# fits
p n
β -β0
0
p n
β Figure 6
-β1
1
We find out the distinction in variation of
such differences for X-flare active region and
flare-quiet active region. The difference
oscillates near zero or in the various half
planes
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